The control problems involved in paper-making processes can be divided into machine-directional (MD) control and cross-directional (CD) control. MD control concerns the paper properties along the direction towards which the paper moves while CD control focuses on the direction that is perpendicular to the machine direction.
CD control aims to reduce the variability of the paper property along the cross direction and to tune the dynamical property to meet the end users' specifications. The paper property is measured by a scanner mounted downstream traversing back and forth across the paper sheet; various feedback control strategies are proposed to achieve consistency of the paper profile. CD control is a challenging control problem that may involves hundreds of process actuators and hundreds or thousands of process measurements, and process models typically have a large amount of uncertainty associated with them. There are spatial and temporal aspects to this problem. The spatial aspect relates to variability of the process measurements across the sheet while the temporal aspect relates to variability of each process measurement over time.
Model predictive control (MPC), a control strategy which takes control and state constraints explicitly into consideration, has seen thousands of applications in industry, and has been recently introduced into CD control in paper-making processes with the advance of computational capability as well as the development of fast QP solvers. The spatially-distributed CD process is a two-dimensional (spatial and temporal) frequency process, and the spatial response and temporal response are decoupled. Consequently, the controller tuning of CD processes can be separated into spatial tuning and temporal tuning. Spatial tuning aims to tune the weighting matrices such that the steady-state paper property across the paper sheet is consistent; temporal tuning concerns more about the satisfaction of performance indices in terms of settling times and control signal overshoots.
Several research results about temporal tuning have been reported. In particular, a constructive procedure to design spatially-distributed feedback controllers has been developed and applied for paper-making processes. Some stability margin and parameter tuning criteria were obtained via rectangular circulant matrices (RCMs) for the unconstrained CD-MPC, which provided a guide in the parameter tuning algorithms. Furthermore, an approximate steady-state performance prediction technique was proposed to speed up the parameter tuning procedure for the constrained CD-MPC. An automated tuning method was presented for the CD process such that the performance and robustness could be simultaneously satisfied under unstructured uncertainty.
As the spatial and temporal aspects of the CD control design are handled independently, robust control performance in the time domain is focused for the temporal aspect. The corresponding design objective is that the control remains temporally stable and the desired CD profile temporal performance is guaranteed in spite of uncertainty about the process model. However, there is lack of an easy-to-use technique to tune a CD controller to provide a robust temporal control performance that is characterized by intuitive indices, e.g., settling time, and to consider parametric model uncertainty, which is easy to understand by the user but is hard to handle for the design.